### 第346課: Decimals & Fractions

In this lesson, we will learn how decimals and fractions are expressed.

### Decimals 小数

A decimal number is a quantity less than 1 but greater than 0 that is expressed without having to use a fraction (分数). In Japan, the decimal point (小数点) is marked with a “．” (ピリオド) as opposed to a comma. The portion of the number to the left of the decimal point is known as the 整数部 (integer portion), and the portion to the right of it is known as the 小数部 (decimal portion).

When reading out decimal numbers, no units are inserted between digits. However, single-mora numbers are often elongated to two morae. As for 0, it is always read as ゼロ. Some speakers may pronounce 4 as しー, but this is no longer common.

No. | Reading |

4.56757 | よん てん ご ろく なな ご（ー） なな |

2.463 | にー てん よん ろく さん |

463.533 | よんひゃくろくじゅうさん てん ご さん さん |

94.02 | きゅうじゅうよん てん れい に |

0.003 | れい てん れい れい さん |

### Fractions

A fraction (分数) is comprised of a numerator (分子) (top part) and a denominator (分母) (bottom part). In English, a fraction such as 3/12 is read as “three twelfths” with the numerator said first followed by the denominator in the plural ordinal form. In Japanese, though, the denominator is stated first, followed by the word 分（ぶん） meaning “portion” and then the numerator.

English | Japanese |

Twelve sixty-forths | ろくじゅうよんぶんの じゅうに |

Seven eighths | はちぶんの なな |

Three and two fourths | さん 【箇・と】よんぶんの に |

In recent decades, the particle と is used to separate the fraction from a whole number. However, older generations were taught to read this as 箇（か）.

### Traditional Decimal Fractions

A decimal fraction is a fraction whose denominator is a power of ten. For instance, 10^-1 is 0.1 written out in decimal notation. Although fractions written out in decimal form are not read out with units, units do exist for decimal fractions. They are used in place of the typical fraction expression.

For example, 1/100 can be expressed as 百分の一, but it can also be expressed as 一厘. In theory, these units could be used with decimal expressions, but past 10^-4, the phrases themselves have practically never been used.

Despite having fallen out of use, the smallest units devised begin to have unstandardized naming conventions.

Unit | Reading | Power of 10 | Decimal Notation |

分 | ぶ | 10^-1 | 0.1 |

厘/釐 | りん | 10^-2 | 0.01 |

毛/毫 | もう | 10^-3 | 0.001 |

糸 | し | 10^-4 | 0.0001 |

忽 | こつ | 10^-5 | 0.00001 |

微 | び | 10^-6 | 0.000001 |

繊 | せん | 10^-7 | 0.0000001 |

沙 | しゃ | 10^-8 | 0.00000001 |

塵 | じん | 10^-9 | 0.000000001 |

挨 | あい | 10^-10 | 0.0000000001 |

渺 | びょう | 10^-11 | 0.00000000001 |

漠 | ばく | 10^-12 | 0.000000000001 |

模糊 | もこ | 10^-13 | 0.0000000000001 |

逡巡 | しゅんじゅん | 10^-14 | 0.00000000000001 |

須臾 | しゅゆ | 10^-15 | 0.000000000000001 |

瞬息 | しゅんそく | 10^-16 | 0.0000000000000001 |

弾指 | だんし | 10^-17 | 0.00000000000000001 |

刹那 | せつな | 10^-18 | 0.000000000000000001 |

六徳 | りっとく | 10^-19 | 0.0000000000000000001 |

虚 虚空 | きょ こくう | 10^-20 | 0.00000000000000000001 |

空 清浄 | くう しょうじょう | 10^-21 | 0.000000000000000000001 |

清 阿頼耶 | せい あらや | 10^-22 | 0.0000000000000000000001 |

浄 阿摩羅 | じょう あまら | 10^-23 | 0.00000000000000000000001 |

涅槃寂静 | ねはんじゃくじょう | 10^-24 | 0.000000000000000000000001 |

1. 五分五分の確率

A 50:50 percentage

2. これは九分九厘（くぶくりん）間違いあるまい！

There is practically (lit. 99%) no doubt about this!

3. あの小旅行での往きの汽車のなかの気楽な対話は、その**八九分**(はっくぶ)を隣りのお喋りや小さな妹たちに負うていたものだとわかった。

I realized that our carefree dialogue on that brief train journey was largely due (lit. 8-90%) to the chatterbox behind us and the two little sisters.

4. 三寸四分五厘

3.45 sun

**Meaning Note**: The 寸 is a length of measurement equivalent to 3.03 cm.

### Percentages with 割

割（わり） is another way of saying 10% and it is frequently used when showing discounts. When used in combination with the decimal fraction units above, the value that they have is practically pushed down a decimal point. However, it is more accurate to interpret something such as 2割3分3厘 as 2.33割 or 23.3% Similarly, this has only ever been extended to the unit 糸.

% | ＋割 | Reading |

10% | 1割 | いちわり |

20% | 2割 | にわり |

30% | 3割 | さんわり |

40% | 4割 | よんわり |

50% | 5割 | ごわり |

60% | 6割 | ろくわり |

70% | 7割 | ななわり |

80% | 8割 | はちわり |

90% | 9割 | きゅうわり |

5. 9割5分

95% or .95

6. 考古学はその7割が図書館内部での調査だ。

70% of archeology is research inside the library.